$(25$ Points$)$ The circular wastewater secondary settling tank of diameter $75$ feet is shown with inflow at the center and is designed to treat a flow of $6$ MGD using a weir trough whose center is inset $5$ feet from the perimeter and whose width is one foot. The mean depth of the tank is $10$ feet.

a$.(10$ points$)$ Determine the hydraulic retention time for the tank in units of hours.

b$.(10$ points$)$ Determine the weir loading rate in units of gallons per day per linear foot.

c$.(5$ points$)$ Determine the critical settling velocity in $gp\frac{d}{f}{t}^2.$